Figure 5.

Invasion of temperate phage with varying degrees of super-infection immunity from $ϵ=0$ (none) to $ϵ=1$ (complete). (A) Example time series of population densities in the case that lytic phage can drive down microbial cell densities so as to enable invasion by temperate phage. Concretely, at time t = 0 h, temperate phage with purely lysogenic strategy cannot invade virus-free environment (first blue diamond); at time t = 200 h, purely lytic phage invade virus-free environment (red circle) and spread; at time t = 600 h, the endemic environment set by the resident lytic strategy can be invaded by temperate phage with purely lysogenic strategy with full immunity ϵ = 1 (see second blue diamond). (B) The invasion fitness (${\mathcal{R}}_{\text{inv}}$) of a temperate phage strategy p_m given variation in ϵ from ϵ = 0 to ϵ = 1, the induction rate is fixed, ${\gamma }_m={10}^{-2}$/h. The model details are presented in Equation (1) and Supplementary Appendix D3, the relevant parameters are selection coefficient ${\alpha }_s=-0.42$ and decay rate of lysogens $d_L=0.5$/h (in the case when prophage impose cost to cellular fitness), influx rate of resources $J=5.33$ ($\mu \mathrm{g}/$ml) h⁻¹, see additional parameters in Supplementary Appendix E.